login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A159969 Numerator of Hermite(n, 13/24). 1
1, 13, -119, -9035, -14639, 10218013, 153914329, -15655840187, -513817209695, 29391432064813, 1713902824372009, -62366587629825323, -6240409786798253711, 134413599620299018045, 25111471036836549128569, -215506510190170502086043, -111283139511606108762536639 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
From G. C. Greubel, Jul 16 2018: (Start)
a(n) = 12^n * Hermite(n, 13/24).
E.g.f.: exp(13*x - 144*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(13/12)^(n-2*k)/(k!*(n-2*k)!)). (End)
EXAMPLE
Numerators of 1, 13/12, -119/144, -9035/1728, -14639/20736, ...
MATHEMATICA
Numerator[Table[HermiteH[n, 13/24], {n, 0, 30}]] (* or *) Table[12^n* HermiteH[n, 1/12], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
PROG
(PARI) a(n)=numerator(polhermite(n, 13/24)) \\ Charles R Greathouse IV, Jan 29 2016
(PARI) x='x+O('x^30); Vec(serlaplace(exp(13*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(13/12)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 2018
CROSSREFS
Cf. A001021 (denominators).
Sequence in context: A367244 A016285 A121086 * A253512 A295048 A295376
KEYWORD
sign,frac
AUTHOR
N. J. A. Sloane, Nov 12 2009
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 13 08:52 EDT 2024. Contains 371638 sequences. (Running on oeis4.)